Great link Fred!
But why do string players (especially cellists, I believe) slightly sharpen the leading note
of an ascending scale, and flatten it on the way down? E.g. the C major scale upwards is
played with a slightly sharp B, and downwards it's played with a slightly flat B. And in so doing,
why is there no disharmony with instruments of fixed pitches playing the same note simultaneously?
One final thought, has a quarter-tone piano ever been made (with 175 keys, presumably)?

Last edited by Timtin on Tue Apr 26, 2011 3:43 pm, edited 1 time in total.

Timtin wrote:Great link Fred!
But why do string players (especially cellists, I believe) slightly sharpen the leading note
of an ascending scale, and flatten it on the way down? E.g. the C major scale upwards is
played with a slightly sharp B, and downwards it's played with a slightly flat B. And in so doing,
why is there no disharmony with instruments of fixed pitches playing the same note simultaneously?

Not just string players, singers do it all the time - because it sounds right.

Timtin wrote:I didn't realise singers did it too, Rob. What I like to know is why it sounds right.

Because Equal Temperament and its variants as used on a piano are compromises. Just Intonation is what is rather more natural and usually feels right, except when placed in an Equal Temperament framework. So singers and string players will often tend toward Just Intonation without perhaps realising it, especially when a particular key or tonal framework is stable. Our chorus master in the Philharmonia will often tell us that our sense of pitch is much better than anything to which the piano is tuned.

I am sure there are others that can explain this rather better than I - perhaps a string player would care to comment?

Thank you Rob. There seems to be quite a lot of literature on this subject.
Presumbly, Thomas Perronet Thompson's book is the just intonation bible.

If one sings (or plays a string instrument) the A major scale down from the A above middle C,
then back up to it, the start and finish frequencies should be 440Hz. But what about the
frequency of the G sharp? According to the Ptolemaic scale, it should be 415.3Hz (I think)
in both directions. But what should it be each way to sound right - 410Hz down and 420Hz up
perhaps? Maybe it's documented somewhere, but not here.

I can only say that the pitches in any scale are altered according to the direction of travel, in an attempt to resolve whatever degree of lack of consonance one is experiencing. What you describe is much like the melodic minor scale, sharpening the 6th & 7th degrees going up and flattening them back going down. http://en.wikipedia.org/wiki/Melodic_minor_scale

I don't know where or even if this is documented, but I have to say that that is what feels right to me. I suspect this is entirely a natural process when the context is stable tonality. We need a string player to discuss this.

The human ear can be trained to accept 'errors' in tonality. A major third at say 400 cents is way off the theoretical 382 cents but we accept it as OK (Bach didn't). If you tune to a different temperament (and I did this to the Young 1799 temperament) the sound and feel are totally different and in some cases awkward to the ear - but after a while the ear becomes attuned to the new paradigm and everything sounds 'normal' again (and equal temperament doesn't!).

So each instrument or voice will be different, and each listener will find each instrument or voice different, so there is no real 'norm' for this. Beauty is in the ear of the beholder.

Thank you Arjuna. I once bought a CD of some Ives quarter-tone 2P music.
It sounded so awful, I got out the scissors and cut it into two pieces!

Going back to this leading note business, which intrigues me greatly, various
overnight thoughts sprang to mind :-
1. In C major, the B natural below it seems to have 3 frequencies, flat for down,
sharp for up, and bang-on for what - trills?
2. Nomenclature - why don't these 3 'notes' have different notation?
3. Can they be detected in isolation i.e. without surrounding notes being played?
4. Disharmony with fixed pitched instruments - already touched upon.
5. Apparent lack of precisely defined frequencies for these lower and higher notes.

Last edited by Timtin on Thu Apr 28, 2011 11:21 am, edited 1 time in total.